In modern days, the ability to carry out computations in parallel is key to efficient implementations of computationally intensive algorithms. This paper investigates the applicability of the previously proposed Augmented Island Resampling Particle Filter (AIRPF) -- an algorithm designed for parallel implementations -- to particle Markov Chain Monte Carlo (PMCMC). We show that AIRPF produces a non-negative unbiased estimator of the marginal likelihood and hence is suitable for PMCMC. We also prove stability properties, similar to those of the $\alpha$SMC algorithm, for AIRPF. This implies that the error of AIRPF can be bounded uniformly in time by controlling the effective number of filters, which in turn can be done by adaptively constraining the interactions between filters. We demonstrate the superiority of AIRPF over independent Bootstrap Particle Filters, not only numerically, but also theoretically. To this end, we extend the previously proposed collision analysis approach to derive an explicit expression for the variance of the marginal likelihood estimate. This expression admits exact evaluation of the variance in some simple scenarios as we shall also demonstrate.

翻译：在现代计算中，并行计算能力是实现计算密集型算法高效实施的关键。本文研究了先前提出的增强型岛屿重采样粒子滤波器（AIRPF）——一种专为并行实现设计的算法——在粒子马尔可夫链蒙特卡洛（PMCMC）中的适用性。我们证明AIRPF可生成边际似然的非负无偏估计量，因此适合用于PMCMC。我们还证明了AIRPF具有与$\alpha$SMC算法相似的稳定性性质。这意味着通过控制有效滤波器数量，可将AIRPF误差随时间均匀有界；而有效滤波器数量可通过自适应约束滤波器间交互来实现。我们从数值与理论两方面证明了AIRPF相对于独立引导粒子滤波器的优越性。为此，我们扩展了先前提出的碰撞分析方法，推导出边际似然估计方差的显式表达式。该表达式在若干简单场景中可实现方差的精确评估，我们亦将对此进行论证。